Chromatic Number Check

Problem

Compute the chromatic number of a small undirected graph: the fewest colors needed for a proper coloring.

Try k = 1, 2, 3, ... and use backtracking with symmetry breaking (a node may only use colors up to the highest already used plus one). Return the smallest feasible k. edges is a list of [u, v] pairs and n is small.

Hint

Symmetry breaking avoids trying color permutations of the same partial coloring.

Test cases

case 1

in: [3,[[0,1],[1,2],[2,0]]]

expected: 3

case 2

in: [4,[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]]]

expected: 4

case 3

in: [4,[[0,1],[1,2],[2,3],[3,0]]]

expected: 2

case 4

in: [5,[[0,1],[1,2],[2,3],[3,4]]]

expected: 2

case 5

in: [3,[]]

expected: 1

Starter codePython

def chromatic_number(n, edges):
    # Your code here
    pass

5 test cases · run your code against them in the editor